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$\int\sin\left(x\right)\left(\sec\left(x\right)+\csc\left(x\right)\right)dx$
Learn how to solve problems step by step online. Integrate the function sin(x)(sec(x)+csc(x)). Find the integral. Rewrite the integrand \sin\left(x\right)\left(\sec\left(x\right)+\csc\left(x\right)\right) in expanded form. Expand the integral \int\left(\sec\left(x\right)\sin\left(x\right)+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\sec\left(x\right)\sin\left(x\right)dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution.