"Find the indefinite integral ∫(4x5−6x+2cos⁡x−4)dx" was answered by our experts

Khaleesi Herbert

Answered question

2021-09-18

Find the indefinite integral

\int (4 x^{5} - 6 \sqrt{x} + 2 \cos x - 4) d x

grbavit

Skilled2021-09-19Added 109 answers

Step 1
Consider the given indefinite integral:

\int (4 x^{5} - 6 \sqrt{x} + 2 \cos x - 4) d x

Here, the objective is to evaluate the given indefinite integral.
Step 2
Re-write the given indefinite integral as:

I = \int (4 x^{5} - 6 \sqrt{x} + 2 \cos x - 4) d x

Use the sum rule of integration

\int (f (x) \pm g (x)) d x = \int f (x) d x \pm \int g (x) d x

I = 4 \int x^{5} d x - 6 \int x^{\frac{1}{2}} d x + 2 \int \cos x d x - 4 \int d x

Use

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C and \int \cos x d x = \sin x + C

I = \frac{4 x^{6}}{6} - \frac{6 x^{\frac{3}{2}}}{\frac{3}{2}} + 2 \sin x - 4 x + C

I = \frac{2 x^{6}}{3} - 4 x^{\frac{3}{2}} + 2 \sin x - 4 x + C

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