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For the following exercises, find the antiderivat…

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Bobby B.

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Problem 377 Problem 378 Problem 379 Problem 380 Problem 381 Problem 382 Problem 383 Problem 384 Problem 385 Problem 386 Problem 387 Problem 388 Problem 389 Problem 390 Problem 391 Problem 392 Problem 393 Problem 394 Problem 395 Problem 396 Problem 397 Problem 398 Problem 399 Problem 400 Problem 401 Problem 402 Problem 403 Problem 404 Problem 405 Problem 406 Problem 407 Problem 408 Problem 409 Problem 410 Problem 411 Problem 412 Problem 413 Problem 414 Problem 415 Problem 416 Problem 417 Problem 418 Problem 419 Problem 420 Problem 421 Problem 422 Problem 423 Problem 424 Problem 425 Problem 426 Problem 427 Problem 428 Problem 429 Problem 430 Problem 431 Problem 432 Problem 433 Problem 434 Problem 435 Problem 436 Problem 437 Problem 438 Problem 439 Problem 440 Problem 441 Problem 442 Problem 443 Problem 444 Problem 445 Problem 446 Problem 447 Problem 448 Problem 449 Problem 450 Problem 451 Problem 452 Problem 453 Problem 454 Problem 455 Problem 456 Problem 457 Problem 458 Problem 459 Problem 460

Problem 399 Medium Difficulty

For the following exercises, find the antiderivatives for the given functions.

$$\cosh ^{2}(x) \sinh (x)$$

Answer

$\frac{\cosh ^{3}(x)}{3}+C$

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Calculus 2 / BC

Calculus

Chapter 6

Applications of Integration

Section 9

Calculus of the Hyperbolic Functions

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Applications of Integration

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Video Transcript

we want to find the anti derivative of Kash squared X times since of X. Now, looking at this, you might notice that we have caution X squared, which is a function square. And then outside of this, well, the driver of a cosh iss cinch which may lead you to thing you need to do a u sub. We could let you equal to caution of X and the derivative of this would be cinch. Sore difference would be d'you use. You just send checks D x then this is exactly what we have there. You go ahead and set the sequel so it be you squared and then this here was exactly d'you. Now we could integrate so integrated that using power rule, we get 1/3 you cute plus C and lastly, we could go ahead and take you. We'll get back in. So that gives us 1/3 caution of X cubed while c so this would be our anti Drew

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Gilbert Strang

Calculus

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